Continuity mistake: When everyone takes food out of the cooler, Bart has a bag of OREOs which magically becomes a bag of different cookies.
Continuity mistake: When the kids wash up on the island after the bus falls into the ocean, we can see they are totally dry. But they were just in water a minute ago, so they should be soaking wet.
Audio problem: When Milhouse is saying he's getting swimmer's ear, his mouth is out of sync whilst saying it.
Audio problem: When the bus is flying off the bridge and Otto says "Which way should I turn?" look closely at him when we can see his face during the line. We can see his mouth is out of sync when he's saying it.
Continuity mistake: When Bart and Nelson first roll the orange and apple, we can see there is no-one sitting in front of Nelson. But a couple of shots earlier, we saw Milhouse sitting in front of Nelson.
Continuity mistake: On the bus, Otto rewinds his tape and there is a shot of the kids. In this shot, we can see the kids and nothing else. A couple of shots later, a food box has appeared out of nowhere.
Revealing mistake: At the U.N. meeting, Bart places his glasses down on the table to read out the Libyan exports. As he puts the glasses down, you can see they are unrealistically floating in the air.
Audio problem: When Homer says God is his favourite fictional character, his mouth is saying something different to what we hear.
Audio problem: When Homer is placing objects on the dining room table to start his website, he is whistling but his mouth isn't moving.
Other mistake: When everyone is eating the boar at the end, the boar is completely intact, yet everyone except for Lisa is seen with a piece of it. (00:20:30)
Continuity mistake: When everyone is running out the cave after finding the boar, Wendell's skin is yellow instead of his usual pale white. (00:19:50)
Continuity mistake: When Bart, Lisa and Milhouse are running away from the others, the order is Bart, then Lisa, then Milhouse. In the next shot it is Lisa, then Bart, then Milhouse. (00:18:45)
Continuity mistake: At Milhouse's trial on the island, Milhouse moves to Lisa so he is at least a foot away from her. In the next shot, Milhouse and Lisa are standing right next to each other. (00:15:25)
Audio problem: When everyone runs towards the cooler on the next morning, they all cheer but their mouths don't move. (00:13:20)
Continuity mistake: When Bart comes out of the water with the cooler, he doesn't have a shirt on. At no point does he put his shirt back on, it reappears when Lisa takes the food off everyone. (00:12:45)
Audio problem: When Bart takes Milhouse's inhaler to go after the cooler, Milhouse says "Hey, I need that to live". His mouth doesn't match with what he is saying. (00:12:15)
Continuity mistake: Just before Bart mentions the Swiss Family Robinson, Lewis is standing in front of him. When Bart mentions the Swiss Family Robinson, Lewis moves further back without enough time for him to move. (00:07:50)
Audio problem: When Bart and Nelson are having a fruit race on the bus, the kids mouths don't move when they are yelling. This occurs in the wide shot. (00:05:40)
Continuity mistake: During the scenes at the site of the mall during the part where they find the Angel, Skinner's hat disappears and reappears.
The Trouble With Trillions - S9-E20
Continuity mistake: In the scene where the FBI agent and Homer are going into the photo booth to view the video, look to the right of the photo booth before they enter. There is a white cup next to the booth. After they have watched the video and are standing outside the booth talking, the cup is now red instead of white.
Answer: I'm not sure if this is the one you're thinking of, but an episode of "Ray Bradbury Theatre," called "A Sound of Thunder," dealt with a similar matter: a group of hunters travel back in time to hunt dinosaurs, only to find things have changed when they get back because someone stepped on a butterfly.
Xofer